Remark : deformation quantization and polarization. In the following section we recall the notion of polarization-depolarization of a product of an algebra. We will see that when we apply this process to an anti-associative algebra \((A,\mu )\) , the associated skew-symmetric map \(\psi \)  defined by \(\psi (x,y)=\mu (x,y)-\mu (y,x)\)  and the symmetric map \(\rho \)  defined by \(\rho (x,y)=\mu (x,y)+\mu (y,x)\) , which provides \((A,\rho )\)  with a Jacobi-Jordan algebra structure, are tied up with the graded Leibniz identity. We develop this point of view in the last section. An algebraic and detailed study of general Jacobi-Jordan algebras is given in [1]}. These algebras are also called mock-Lie algebras [2]}.
